Hey, I'm new here, so it's possible this theory has been discussed already, but here it is.
My idea is that Honor/The Almighty/Tanavast was the Shardbearer that Kaladin killed.
Evidence:
1. Look at Cenn's description of what happens in the beginning of the book. First, thunder for no apparent reason. "He could hear faint thunder. That was odd. The sky was cloudless." Then, a Shardbearer appears out of nowhere. He is "in gleaming armor that seemed to radiate light." "The plate was gilded." Then the kicker: "It was like...like the Almighty himself had taken form to walk the battlefield." That really got my attention.
2. Kaladin, while in the slaver caravan, thinking back on what happened with Amaram, thinks this: "Were there men who had honor. No, Kaladin thought. Honor died eight months ago." This could be a clue from BS that the shard Honor literally did die eight months ago, on the battlefield.
3. When Amaram comes to talk to Kaladin and kill his men, he enters in the middle of a conversation. "'...why Thaidakar would risk this?' Amaram was saying, speaking in a soft voice. 'But who else would it be? The Ghostbloods grow more bold. We'll need to find out who he was. Do we know anything about him?' 'He was Veden, Brightlord,' the stormwarden said. 'Nobody I recognize.'" Nobody knows who the Shardbearer is. He seems to come out of nowhere.
4. Dalinar's talk with the Almighty at the end has a few different things. "He had dark skin and pure white hair...[his clothing] seemed made of gold." Remember the plate that was gilded? Just a thought. I don't remember what Vedens look like, but if they have dark skin or light hair or both, that would be more evidence. Also, he says "I am dead. Odium has killed me." See the next point.
5. Looking at the actual scene of the death, there are some more interesting things. Again, the gold armor. Kaladin also describes him as a "beautiful divinity," another description of him being god-like. Then, when the Shardbearer kills Cenn, Dallet, and others, Kaladin decides to go after him. "Anger boiled inside of Kaladin." "Was he running to get vengeance, or was he trying to protect his highmarshal?...Did it matter?" He is filled with hatred, and doesn't really care why he's doing what he's doing. Then, when the Shardbearer kills almost all the rest of his men, you can really see it. "Something drove him forward, against all logic, against all sense. Sickened, agonized, enraged." The definition of odium is hatred or rage. (also, the shame and hatred involved in a dishonorable act, but that's not the sense I'm using here) I would suggest that Odium influences Kaladin here to kill Honor. Just as insane people are more easily influenced by Ruin on Scadrial, Odium would be able to control to some extent people who are feeling hatred. Kaladin, as he has lost his friends and the people he tried to protect for so long is very vulnerable. When it says that something else drove him to do it, that says to me that Odium was influencing him. In that way, Odium killed Honor through Kaladin.
If anyone could contribute any further evidence, (what do Vedens look like, or anything else) or criticism, I would appreciate it.